Expression of type ExprTuple

from the theory of proveit.logic.sets.comprehension

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, ExprRange, ExprTuple, IndexedVar, Lambda, S, Variable, n, x
from proveit.core_expr_types import R__x_1_to_n, f__x_1_to_n, x_1_to_n
from proveit.logic import And, InSet
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(Lambda([x_1_to_n], Conditional(f__x_1_to_n, And(ExprRange(sub_expr1, InSet(IndexedVar(x, sub_expr1), IndexedVar(S, sub_expr1)), one, n), R__x_1_to_n))))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(\left(x_{1}, x_{2}, \ldots, x_{n}\right) \mapsto \left\{f\left(x_{1}, x_{2}, \ldots, x_{n}\right) \textrm{ if } \left(x_{1} \in S_{1}\right) ,  \left(x_{2} \in S_{2}\right) ,  \ldots ,  \left(x_{n} \in S_{n}\right) ,  R\left(x_{1}, x_{2}, \ldots, x_{n}\right)\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 12 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 12
4	Operation	operator: 6 operands: 7
5	Variable
6	Literal
7	ExprTuple	8, 9
8	ExprRange	lambda_map: 10 start_index: 18 end_index: 19
9	Operation	operator: 11 operands: 12
10	Lambda	parameter: 25 body: 13
11	Variable
12	ExprTuple	14
13	Operation	operator: 15 operands: 16
14	ExprRange	lambda_map: 17 start_index: 18 end_index: 19
15	Literal
16	ExprTuple	21, 20
17	Lambda	parameter: 25 body: 21
18	Literal
19	Variable
20	IndexedVar	variable: 22 index: 25
21	IndexedVar	variable: 23 index: 25
22	Variable
23	Variable
24	ExprTuple	25
25	Variable